Cauchy Euler, non-homogeneous, weird condition

xy''+y'=-x
y(1)=0, y(0) bounded (so the natural log, 1/x etc. terms drop out)
homogeneous, cauchy euler: y=a+bx
variation of parameters, and using the conditions gives y=1-x, I think (i tried this previously and I think this is what I got, I didnt write it down). Very different from what I have on my solution handout.
First off, does it matter when to apply the bounded condition? (as in, do we drop the blnx term first? the problem here is variation of parameters doesnt work then),
Is there another way to solve a non-homogeneous cauchy euler besides using variation of parameters?

Man..thanks Tim I see that now. Very easy once that is spotted.
I tried over and over to solve this as a cauchy euler, then using variation of parameters; would that approach be invalid? I couldnt get the answer.

If you want someone to point out what you did wrong, then you will have to show what you did! I did this problem using "variation of parameters" and I certainly got nothing involving "[itex]x^3[/itex]".

homogeneous: xy''+y'=0 make substitution y=x^r, so homogeneous soln is y=a+blnx (call it yc)
variation of parameters:
u1'=a determinant with entries (from left to right, top to bottom) 0, lnx, -x, 1/x then divide that by the wronskian= 1/x
u2'= a determinant with entries (from left to right, top to bottom) 1, 0, 0 -x, then divide by wronskian= 1/x
u1= x^3/3*lnx-x^3/9 u2=-x^3/3
yp=u1*1+u2*lnx
y=yc+yp

homogeneous: xy''+y'=0 make substitution y=x^r, so homogeneous soln is y=a+blnx (call it yc)

Okay, the characteristic equation is [itex]r^2= 0[/itex] which has r= 0 as a double root. That gives the general solution to the associated homogeneous equation, y= a+ b ln(x).

variation of parameters:
u1'=a determinant with entries (from left to right, top to bottom) 0, lnx, -x, 1/x then divide that by the wronskian= 1/x
u2'= a determinant with entries (from left to right, top to bottom) 1, 0, 0 -x, then divide by wronskian= 1/x
u1= x^3/3*lnx-x^3/9 u2=-x^3/3
yp=u1*1+u2*lnx
y=yc+yp

But this is wrong; what am I doing wrong?

Using "variation of parameters", we look for a solution of the form y(x)= u1(x)ln(x)+u2(x). Then y'= u1'ln(x)+ u1/x+ u2'. Because there are, in fact, an infinite number of such solutions, we narrow the search and simplify by requiring that u1'ln(x)+ u2'= 0. Then y'= u1/x so that [itex]y''= u'/x- u/x^2[/itex].

Thanks.
I learned a different method (or different way of viewing it anyway) for variation of parameters, and actually it required diving out the lead coefficient before beginning to solve for the particular solution. Everything's good now.